The proof of the above uses the following lemma from [1]} which is based on the reduction from Unique Games to SmallSetExpansion. Towards stating the lemma, let us introduce the noise operator \(T^V_{1 - \eta }\)  in the product space \(V^R\)  which is defined as follows. For \(A \in V^R\) , \(\tilde{A} \sim T^V_{1 - \eta }(A)\)  is sampled as follows. For every \(i \in [R]\) , do the following independently: with probability \(1 - \eta \) , set \(\tilde{A}(i) = A(i)\) , and with probability \(1 - \eta \) , set \(\tilde{A}(i) \sim V\) .
